ArticleNature communications2021
Physics-informed learning of governing equations from scarce data.
Article in Nature communications, 2021. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 53 papers.
What it found
Each row is one number read from the abstract, on the scale the paper reported it, with its interval. Left of the dashed line favours the treatment, right favours the comparator. Under each row is the sentence it came from. New to these charts? A ten-minute tutorial.
The abstract states no effect estimate the extractor could read, or names no intervention and outcome on the map, so this paper lights no cell and moves no belief. It is still indexed, cited and linked below.
The trial behind it
Trials whose registry record cites this paper, or whose number appears in the abstract. A trial that started after this paper was published is citing it as background, not reporting it.
Neither the registry nor the abstract names a trial number. If this is a trial report, that itself is worth knowing.
Who cites it
53 citing papers in PubMed.
- Physics informed neural network framework for non-similar nano-heat and solutal transport in a rheological fluid over a stretching cylinder.Discover nano · 2026Article
- Leveraging Machine Learning for Accelerated Electrode-Electrolyte Interface Design in Rechargeable Li-Based Batteries.Small (Weinheim an der Bergstrasse, Germany) · 2026Review
- Toward nonlinear representations with Gaussian-splat manifolds for physics-informed learning.Nature communications · 2026Article
- From data chaos to physically interpretable deterministic mapping.Nature communications · 2026Article
- A physics-informed foundation model for rapid high-fidelity structural response prediction.Nature communications · 2026Article
- End-to-end robust system discovery in electrical dynamical systems using scientific machine learning.Communications engineering · 2026Article
- Moving from table to graph in physics-informed spatio-temporal symbolic regression.Scientific reports · 2026Article
- Advances and future directions in identifying specific taxa from microbial meta-omics data: from pipeline to deep learning.mSystems · 2026Review
- Encoding Cumulation to Learn Perturbative Nonlinear Oscillatory Dynamics.Advanced science (Weinheim, Baden-Wurttemberg, Germany) · 2026Article
- Physics-informed structural diagnostics of model-data agreement beyond scalar metrics.Scientific reports · 2026Article
- Gradient-Driven Physics Informed Neural Networks for Conduction Heat Transfer and Incompressible Laminar Flow.Journal of computational and nonlinear dynamics · 2026Article
- Optimising pandemic response through vaccination strategies using neural networks.Scientific reports · 2026Article
- Ultraprecision, high-capacity, and wide-gamut structural colors enabled by a mixture probability sampling network.Light, science & applications · 2026Article
- AI for atmosphere-ocean sciences: advancements, challenges and ways forward.National science review · 2026Review
- Hybridndiff-UQ: Uncertainty quantification for hybrid neural differentiable modeling.Theoretical and applied mechanics letters · 2026Article
- Multi-Objective Spray Drying Process Optimization via BBD-ANN-AGWO Framework: Case of Andrographolide Amorphous Solid Dispersions.AAPS PharmSciTech · 2026Article
- Reconstructing Actin Dynamics of the Leading Edge from Observational Data.bioRxiv : the preprint server for biology · 2026Article
- Knowledge integration for physics-informed symbolic regression using pre-trained large language models.Scientific reports · 2026Article
- Artificial Intelligence-Enhanced Wearable Blood Pressure Monitoring in Resource-Limited Settings: A Co-Design of Sensors, Model, and Deployment.Nano-micro letters · 2026Review
- Discovering physical laws with parallel symbolic enumeration.Nature computational science · 2026Article
Corrections and comments
PubMed lists nothing against this paper. Absence here is not a guarantee, only a check that was made.
Authors and funding
3 authors.
Funding
Abstract
Harnessing data to discover the underlying governing laws or equations that describe the behavior of complex physical systems can significantly advance our modeling, simulation and understanding of such systems in various science and engineering disciplines. This work introduces a novel approach called physics-informed neural network with sparse regression to discover governing partial differential equations from scarce and noisy data for nonlinear spatiotemporal systems. In particular, this discovery approach seamlessly integrates the strengths of deep neural networks for rich representation learning, physics embedding, automatic differentiation and sparse regression to approximate the solution of system variables, compute essential derivatives, as well as identify the key derivative terms and parameters that form the structure and explicit expression of the equations. The efficacy and robustness of this method are demonstrated, both numerically and experimentally, on discovering a variety of partial differential equation systems with different levels of data scarcity and noise accounting for different initial/boundary conditions. The resulting computational framework shows the potential for closed-form model discovery in practical applications where large and accurate datasets are intractable to capture.
Identifiers
What OpenQuestion holds
Registered trials
Read under generation 80e0d062 · epoch 390. Bibliography from PubMed, PubMed Central and OpenAlex; grants from NIH RePORTER; trial links from ClinicalTrials.gov; estimates, votes and beliefs from the OpenQuestion graph.